It is known to cause electromagnetic radiation to interact with a sample to obtain data which determines Ellipsometric Parameters, as a function of wavelength and/or angle-of-incidence, and then to perform mathematical regression of a proposed mathematical model of said sample onto values for ellipsometric PSI and DELTA to obtain values of, for instance, thickness and optical constants, where said ellipsometric PSI and DELTA are identified by:ρ=rp/rs=Tan(Ψ)exp(iΔ)
In most cases the regression procedure is successful in providing useful information without the need to pre-condition data to reduce the effects of noise therein. In some cases, however, where it is desired to determine such as a pseudo-“n” and/or pseudo-“k” value of a sample at a specific wavelength, the presence of noise can be a significant source of uncertainty. (Note, pseudo-“n” and pseudo-“k” refer to “n” and “K” for a sample investigated as a monolithic whole, without taking into account specific structure). The disclosed invention provides an approach to overcoming such data analysis difficulty without the need to develop an accurate mathematical model for a sample structure.
A Search for relevant patents, provided a patent to Johs et al., U.S. Pat. No. 5,872,630, from which the present Application is derived as a CIP via intervening CIP Applications. Said 630 patent primarily describes a spectroscopic rotating compensator material system investigation system. Amongst other disclosure said 630 patent describes a Mathematical Regression based Calibration procedure which makes possible the use of essentially any compensator regardless of non-achromatic characteristics. And specifically, parameterization of variables was disclosed as an approach to optimizing use of information available in a data set. The basic concept of the presently Claimed approach to minimizing the effects of noise in data, in the context of data obtained from the practice of ellipsometry, was established and disclosed in said 630 patent which was Filed Aug. 15, 1997.
Additional demonstrative patents which disclose use of a spectroscopic range of wavelengths were also identified as follows.
A patent to Johs, from which the 630 patent was Continued-in Part, is No. 5,666,201, filed Sep. 20, 1995. The focus in said 201 patent comprises a detector arrangement in which multiple orders of a dispersed beam of electromagnetic radiation are intercepted by multiple detector systems.
U.S. Pat. No. 5,706,212, Issued Jan. 6, 1998, and Filed Mar. 20, 1996 for an Infrared Ellipsometer System Regression based Calibration Procedure. Said 212 patent describes use of an Substantially Achromatic Rotating Compensator and application of Mathematical Regression in a Calibration procedure which evaluates calibration parameters in both rotating and stationary components. The 212 patent describes that 2ωMEGA and 4ωOMEGA associated terms are generated by a detector of a signal which passes through a compensator caused to rotate at a rate of OMEGA. Said 630 patent was Continued-in-Part therefrom, as is the present application via an intervening patent application.
A patent to Chen et al., U.S. Pat. No. 5,581,350 is identified as it describes the application of regression in calibration of ellipsometer systems similar to that described in a paper by Johs in 1993.
Other patents are identified as generally describing ellipsometry systems which contain means which can generate data containing systematic or random noise, to which the disclosed invention can be applied.
Patents to Aspnes et al. are Nos. 6,320,657 B1, 6,134,012, 5,973,787 and 5,877,859. These patents describe a Broadband Spectroscopic Rotating Compensator Ellipsometer System wherein the Utility is found in the use of a “substantially Non-Achromatic” compensator and selecting a Wavelength Range and Compensator so that “an effective phase retardation value is induced covering at least from 90 degrees to 180 degrees”, (012 patent), over a range of wavelengths of at least 200-800 nm. The 787 and 859 recite that at least one wavelength in said wavelength Range has a retardation imposed of between 135 and 225 Degrees, and another wavelength in the wavelength Range has a retardation imposed which is outside that retardation Range.
A recently published PCT Application is No. WO 01/90687 A2, which is based on U.S. application Ser. No. 09/575,295 filed May 3, 2001. This application was filed by Thermawave Inc. and specifically describes separate use of a 2ω and a 4ω term to provide insight to sample thickness and temperature.
Two patents which identify systems which utilize Polychromatic light in investigation of material systems, U.S. Pat. Nos. 5,596,406 and 4,668,086 to Rosencwaig et al. and Redner, respectively, were also identified.
Also identified is a patent to Woollam et al, U.S. Pat. No. 5,373,359 as it describes a Rotating Analyzer Ellipsometer System which utilizes white light. Patents continued from the 359 Woollam et al. U.S. Pat. Nos. 5,504,582 to Johs et al. and 5,521,706 to Green et al. Said 582 Johs et al. and 706 Green et al. patents describe use of polychromatic light in a Rotating Analyzer Ellipsometer System.
As the disclosed invention contemplates use of focused and non-focused beams of electromagnetic radiation, patents which describe means for focusing in ellipsometer systems were also identified.
A PCT Patent Application, No. WO 01/086257 is also known and is disclosed as it describes a combination of an aperture and lens to define a spot on a sample.
A patent to Lacey et al., U.S. Pat. No. 5,793,480 is disclosed as it describes a field stop and lens combination in an ellipsometer prior to a sample.
A patent to Spanier et al., U.S. Pat. No. 5,166,752 is disclosed as it describes an ellipsometer with lenses and apertures before and after a sample.
Regarding Articles, an article by Johs, titled “Regression Calibration Method For Rotating Element Ellipsometers”, which appeared in Thin Film Solids, Vol. 234 in 1993 is also identified as it predates the Chen et al. patent and describes an essentially similar approach to ellipsometer calibration.
A paper by de Nijs et al., titled “Systematic and Random Errors in Rotating-Analyzer Ellipsometry”, Optical Society of America, Vol. 5, No. 6 (1988), which identifies two types of errors, (ie. random and systematic).
A book by Azzam and Bashara titled “Ellipsometry and Polarized light” North-Holland, 1977 is disclosed and incorporated herein by reference for general theory.
As well, identified for authority regarding regression, is a book titled Numerical Recipes in “C”, 1988, Cambridge University Press.
A need exists for a method of evaluating dependent variables which can be represented as a function of an independent variable in a mathematical function, based upon data which contains noise.